Wave filter



1937- R. B. BLACKMAN 2,091,250

WAVE FILTER Filed Aug. 13, 1935 REACTANCE FREQUENCY /NVEN7'OR 1 yRBBLACKMAN Z-MM ATTORNEY Patented Aug. 31, 1937 UNITED STATES PATENTOFFICE WAVE FILTER Ralph E. Blackman, Rutherford, N. J., assignor toBell Telephone Laboratories,

Incorporated,

8 Claims.

This invention relates to impedance elements for use in wave filters andmore particularly to impedance elements of the electromechanical type inwhich a mechanical vibrator coupled to an electrical circuit produces areaction therein by virtue of its coupling thereto.

The principal object of the invention is to improve the efiiciency andthe frequency characteristics of electromechanical vibrators intendedfor operation at relatively high frequencies, for example thefrequencies of carrier telephony. Another object is to improve andsimplify the construction of mechanical vibratory systems havingrelatively complex resonance characteristics.

These objects are achieved by combining mechanical transmission lines,forming the mechanical vibratory portion of an electromechanicalimpedance, in such a way that wave reflection effects at their junctiongive rise to additional resonances at predetermined frequencies. By theuse of structures particularly adapted to transmit longitudinalmechanical waves, either compressional or torsional, simple and ruggedvibratory systems are made available for operation at the frequencies ofcarrier telephony and by utilizing materials, such as brass, aluminum orglass, which are characterized by extremely low dissipation, theefliciency of the vibratory system is greatly improved.

The nature of the invention will be more fully understood from thefollowing detailed description and by reference to the attached drawing,of which:

Fig, 1 is a view partly in section of one embodiment of theelectromechanical impedance element of the invention;

Fig. 2 is a diagrammatic representation showing how two of the impedanceelements of Fig. 1 may be utilized in a wave filter of the lattice type;

Fig. 3 shows reactance characteristics to which reference is made inexplaining the invention;

Fig. 4 shows diagrammatically the reactance characteristics of thebranches of the lattice network of Fig. 2; and

Fig. 5 is a diagram of a typical attenuation characteristic obtainablewith the filter of Fig. 2.

Fig. 1 shows, partly in section, one embodiment of the electromechanicalimpedance element of the invention in which the mechanical vibrator llcomprises a central portion [2 and two symmetrical end portions I3having a cross-sectional area difiering from that of the centralportion. The cross-sections of these portions of the vibrator may beround or of any other convenient shape, and their areas and the lengthsof the sections are proportioned to produce desired resonancecharacteristics. The vibrator is preferably made of non-magneticmaterial having 2. low dissipation constant, such, for example, asbrass, aluminum or glass. The vibrator is longitudinally symmetricalabout a central plane by the line [4, l4 and when driven in the mannerexplained below it will have a nodal region coinciding with this planeof symmetry. In order to permit unrestricted vibration the vibrator ispreferably supported at or near this nodal region. As shown in thefigure, this may be done by means of a flange [5 which may be made anintegral part of the mid-section 12. The flange may be clamped betweenthe two parts l6 and i! of the outer casing, or supported in any othersuitable manner.

The vibrator is set into vibration by means of two similarelectromagnetic drives, one being located at each end. Each of thesedrives comprises a magnetic armature l8, secured to the end of thevibrator, a permanent magnet I 9, two pole-pieces 20 and 2| and adriving coil 22. The assembly is enclosed within the housing M and thelead wires to the coils are introduced through the insulating bushings41. When oscillatory currents equal in magnitude but opposite in phaseare impressed upon the two sets of coil terminals 23, 2 5 and 25, 26,respectively, mechanical forces of equal magnitude but of opposite phaseare impressed upon opposite ends of the vibrator, and longitudinalcompressional mechanical waves are produced therein.

Fig. 2 is a schematic diagram showing how two electromechanicalimpedances 2'! and 28 of the type described above may be connectedbetween a pair of input terminals 29 and 3D, and a pair of outputterminals 3| and 32 to form a band-pass wave filter of the symmetricallattice type. The impedance 21 has terminals 33, 34, 35 and 3G, and theimpedance 28 has terminals 31, 38, 39 and 40, corresponding,respectively, to terminals 23, 25, 24 and 26 shown in Fig. 1. Each ofthe impedances is shown within a dotted enclosure, in the interest ofclarity. The terminals 33 and 35 of the impedance 2! are connectedbetween terminals 29 and 3|, and the terminals 34 and 36 betweenterminals 30 and 32 to form the two series impedance branches of thelattice network. Similarly, terminals 40 and 38 of the impedance 28 areconnected between terminals 29 and 32, and terminals 31 and 39 betweenterminals 3! and 30 to form the diagonal branches of the latticenetwork. In this way a single electromechanical impedance is made toprovide a pair of impedance branches in the lattice. To equalcapacitances C1, C1 may be connected, respectively, in series with theterminals 35 and 36 and a second pair of equal capacitances C2, C2 maybe connected in series with the terminals 31 and 38 in order to improvethe transmission characteristics of the filter, as explainedhereinafter.

The nature of the impedance characteristic obtainable with this type ofelectromechanical impedance element will now be considered. Themechanical input impedance Z of a rod of nonuniform cross--section, suchas the vibrator ll, when the driving forces at the two ends are in phaseopposition is the same as that of a rod of the length of one of the endsections l3 connected in tandem with a rod of half the length of themid-section E2, the latter being fixed at its distant end. If thevibrator is driven from one end only, a standing wave is set up thereon,and in general the central plane will be in motion. If new the drivingforce be removed from the first end and applied to the other end of thevibrator the same type of wave will be set up therein but thedistribution of the motion will be inverted with respect to the centralplane. However, if equal driving forces be applied to both endssimultaneously and in such a way that both of the armatures 58 areattracted or both are repelled at the same time the motion at the centerdue to the two forces will completely cancel out, leaving the centralplane at rest, regardless of the frequency impressed upon the ends.Under these conditions the mechanical forces impressed upon the rod maybe said to be in phase opposition.

It follows, therefore, that so far as the input impedance is concernedthe vibrator may be considered to be fixed at its center. The impedancewill be the same as that of a mechanical transmission line consisting ofa section equal in length to the end section l3 in series with a secondsection of half the length of the central section if,

the latter being fixed at its distant end and con-- sequently terminatedin the equivalent of an infinite impedance. Following Equation (33)given on page 113 of Sheas Transmission Networks and Wave Filters,published by D. Van Nostrand Company,'the input impedance of such asystem may be expressed as Z -I- K1 tanh P1 K +z, tanh P (1) in which K1and Pr are the characteristic impedance and transfer constant,respectively, of an end section it, and Zr is the terminating impedanceof the end section. The characteristic impedance K and the transferconstant P of a rod, assuming that the elastic waves are propa" gatedwith a plane wave front normal to the axis, may be found from thefollowing express1ons:

P: am/

in which A represents the cross-sectional area, p is the density of thematerial, E is Youngs modulus of elasticity, l is the length of the lineand denotes the frequency multiplied by Z-rr.

Since the end section is connected in tandem with the mid-section, andthe latter is effectively opencircuited at its distant end, theimpedance Zr is given by the equation in which K2 and P2 are thecharacteristic impedance and transfer constant, respectively, of half ofthe mid-section l2. Equation (2) is obtained by setting up an expressionfor the input impedance of the mid-section, similar in form to equation(1), and substituting therein the value of which, when numerator anddenominator are divided by tanh P1, leads to the expression K Kg 2 tanhP tanh P 1 2 tanh P tanh P The impedance Z may be considered to be madeup of the series connection of two impedances Z1 and Z2 corresponding tothe two terms on the right-hand side of Equation (4). The first of thesetwo impedances, corresponding to the first term, is

K K tanh P tanh Pg (5) 1 K1 K2 tanh P tanh Pg which will be recognizedas the impedance of two open-circuited, uniform transmission linesconnected in parallel. When dissipation is neglectsuch a transmissionline is periodically resonant at some frequency f and at every oddmultiple thereof, and is anti-resonant at zero frequency and every evenmultiple of f. In the special case where the two lines in parallel havethe same transfer constants, that is, when P1: P2, the criticalfrequencies of one will coincide with those of the other, and thecombined impedance will be of the same form as the impedance of onealone. Such an impedance characteristic is shown by the dotted curve 9.2of Fig. 3 for the frequency range from zero to 3 The impedance Z2,corresponding to the second term, is

tanh P tanh P Multiplying both numerator and denominator by tanh P tanhP gives K 2 K tanh P K I? tanh P K 2 K tanh P +K tanh P This will berecognized as the parallel impedance of two short-circuited lines, onehaving the parameters K1 and P1 and the other having the parameters K2and P2, the latter being viewed through an ideal transformer having aturns ratio of K1 to K2. A uniform transmission line short-circuited atits remote end will have antiresonances at the frequency f and oddmultiples thereof, and resonances at zero frequency and even multiplesof f. If two such lines have equal transfer constants, their parallelimpedance will have a reactance characteristic of the type shown bydotted curve 43 of Fig. 3.

The mechanical impedance Z of the vibrator l I, which, as explainedabove, may be considered to be made up of the two series impedances Z1and Z2, will therefore be the algebraic sum of the two curves 42 and 43,and will be of the form shown by the solid line curve 44 of Fig. 3,having anti-resonances at the frequencies zero, 1, 2f and 3 andresonances at the frequencies f1, f2 and f3.

The armature [8, considered as a lumped mass, will not change thelccation of the anti-resonances but will cause each resonance to occurat a somewhat lower frequency. The magnetic field surrounding thearmature exerts a force of attraction which increases more and morerapidly as the armature approaches the pole-pieces and is in effect anegative stiffness which willfurther lower each resonance frequency. Theelectrical impedance of the system at this point will be just theinverse of the mechanical impedance described above, resonancesoccurring where anti-resonances are located in the mechanical impedance,and vice versa. In this connection reference is made to United StatesPatent No.

1,642,506 to E. L. Norton issued September 13,

1927. The damped inductance of the driving coils 22, since they appeareffectively as series elements, will cause each resonance to move downto a lower frequency but will not displace the anti-resonances. Theaddition of the capacitances C1 or C2 will move each resonance to ahigher frequency and will introduce an antiresonance at zero frequency.The resulting electrical impedance of the entire system is of the formshown by the solid line curve of Fig. 4, having an anti-resonance atzero frequency, one at It slightly below I and a third at f7 slightlyabove I, and two resonances f4 and is falling below f and a third at f8between 1 and 2 The next anti-resonance, not shown on the diagram, will1 fall at a frequency at least as high as 3f5.

Curve 45 may represent, for example, the impedance of the element 2'! ofFig. 2, in combina- 40 tion with the capacitances Cl. A secondelectromechanical impedance, such as 28 of Fig. 2, with its associatedcapacitances C2, may be designed to have resonances at the frequenciesf5, f7 and f9, and anti-resonances at the frequencies zero, 4.3 ft andfa, as shown by the dotted curve 46 of Fig. 4.

Two such impedances may be arranged, as explained above in connectionwith Fig. 2, to form a lattice type band-pass wave filter. Thetransmission band will be located between the fre- 5 quencies f4 and f9where the two reactances are of opposite sign, and peaks of attenuationWill occur at the frequencies ha and hi where the two curves cross eachother. The transmission characteristic is shown diagrammatically by Fig.5. Other attenuation peaks, not shown, may be located either above orbelow the transmission band.

The use of vibrators having non-uniform crosssections, it will be noted,permits the building of Of) wave filters having added resonances andanti-- resonances occurring within the transmission band. These addedcritical frequencies may be utilized to broaden the transmission bandand to introduce additional peaks of attenuation in the attenuatingregions. Also, the use of material having a low dissipation constantreduces the loss and distortion in the transmission band and increasesthe height of the attenuation peaks.

What is claimed is:

71: 1. In an electric wave filter, an electromechanical impedancecomprising, as a mechanical vibratory element, a rod of elastic materiallongitudinally symmetrical about its middle section, the material ofsaid rod having a low dissipation constant and said rod comprising aplurality of portions of different cross-sectional areas the lengths andcross-sections of which are proportioned to produce a plurality ofmechanical resonances located within the transmission band of saidfilter at frequencies unharmonically related to each other andrelatively close together in order to broaden said band and increase thediscrimination, means for supporting said rod at its middle section,similar electromagnetic driving means disposed at each end of said rodand adapted to produce longitudinal mechanical waves in said rod inresponse to oscillatory electric currents, and circuit connectionsbetween said driving means whereby the mechanical forces impressed onthe opposite ends of said rod are equal in magnitude and opposite inphase.

2. In an electric wave filter an electromechanical impedance inaccordance with claim 1 in which the electromagnetic driving means areadapted to produce longitudinal compressional waves in the driven rod.

3. In an electric wave filter, an electromechanical impedance inaccordance with claim 1 in which the mechanical vibratory elementcomprises a rod of non-magnetic material and magnetic armatures at eachend of said rod, said armatures forming part of the said electromagneticdriving means and being disposed to produce longitudinal compressionalwaves in said rod.

4. An electromechanical impedance in accordance with claim 1 in whichthe mechanical vibratory means comprise a rod of non-magnetic metal andin which the supporting means for said rod comprise a flange integralwith said rod at the mid-section thereof.

5. In an electric wave filter, an electromechanical impedancecomprising, as a mechanical vibratory element, a rod of non-magneticelastic material longitudinally symmetrical about its middle section,said rod comprising a plurality of portions of difierent cross-sectionalareas the lengths and cross-sections of which are proportioned toproduce a plurality of mechanical resonances located within thetransmission band of said filters at frequencies unharmonically relatedto each other and relatively close together in order to broaden saidband and increase the discrimination, means for supporting said red atits middle section, similar electromagnetic driving means disposed ateach end of said rod and adapted to produce longitudinal mechanicalwaves in said rod in response to oscillatory electric currents, andcircuit connections whereby said driving means are adapted to impressforces of opposite phase on said rod.

6. An electromechanical impedance in accordance with claim 5 in whichthe said electromagnetic driving means are adapted to producelongitudinal compressional waves in said rod.

7. An electromechanical impedance in accordance with claim 5 in whichthe several portions of the said rod are of like cross-sectional formand are of equal length.

8. An electromechanical impedance in accordance with claim 5 in whichthe several portions of the said rod are of circular cross-section andare of equal lengths.

RALPH B. BLACKMAN.

